Explanation Given: Function is f ( x ) and constant is k . Calculation: Consider F ( x ) is an anti-derivative of f ( x ) . F ′ ( x ) = f ( x ) Multiply by constant k in above equation as follows: k f ( x ) = k F ′ ( x ) = ( k F ′ ( x ) ) Thus, k F ′ ( x ) is an anti-derivative of k f ( x )

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.4, Problem 76P

To determine

To prove: ∫kf(x)dx=k∫f(x)dx .

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Chapter 4.4, Problem 75P

Chapter 4.4, Problem 77P

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Chapter 4 Solutions

Calculus

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To prove : ∫ k f ( x ) d x = k ∫ f ( x ) d x .

Solution Summary: The author explains how the function f(x) is an anti-derivative of the constant k in the equation.

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To prove: ∫kf(x)dx=k∫f(x)dx .

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Chapter 4 Solutions